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As far as I know, heat radiation is caused by the electromagnetic waves produced by the permanent or induced dipoles of the heated material. The higher the heat, the higher the frequency of oscillation and as such, the higher the frequency of the electromagnetic waves. My question is, why do the molecules oscillate at a higher frequency when exposed to higher temperatures?

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  • $\begingroup$ Are you familiar with Equipartition theorem? Temperature is essentially the measure of how much vibration the molecule is showing (in this case) $\endgroup$
    – Cryo
    Jan 4, 2021 at 9:15
  • $\begingroup$ No, not familiar with this theorem, but I will check it out @Cryo, thanks $\endgroup$
    – A. Kvåle
    Jan 4, 2021 at 9:33

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Temperature is, at least in classical mechanics (to the best of my knowledge), an emergent property of all the particles in a substance defined by the average random kinetic energy of the particles in the substance.

A temperature increase, then, can be taken as a direct indication that the random kinetic energy of the particles, which relates to the energy with which the particles oscillate, has increased. If the particles are oscillating with greater energy, it is implied that any individual particle is oscillating at a higher frequency (provided you take that particle to be a simple harmonic oscillator).

The equation that relates the oscillating "angular speed" $\omega$ of a simple harmonic oscillator (i.e. a given molecule) to its energy of oscillation is $$E = \frac{1}{2}m\omega^2 x_0^2$$ where $x_0$ is the amplitude (max. displacement) of oscillation, and $m$ is the oscillator's mass. The mass of the oscillator will not (appreciably) change when it oscillates with more energy, as nothing is really happening to the molecule. $x_0$ will not change significantly, given that the molecule is surrounded by neighbors in some larger structure, like a solid or liquid. As such, the only element of its oscillation that can change is $\omega (= 2\pi f)$ - its angular speed (proportional to its frequency) - such that it oscillates faster.

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